The Reaction - Diffusion Front for A + B → ∅ in One Dimension

We study theoretically and numerically the steady state diffusion controlled reaction A + B → ∅, where currents J of A and B particles are applied at opposite boundaries. For a reaction rate λ, and equal diffusion constants D, we find that when λJ −1/2 D −1/2 ≪ 1 the reaction front is well described by mean field theory. However, for λJ −1/2 D −1/2 ≫ 1, the front acquires a Gaussian profile-a result of noise induced wandering of the reaction front center. We make a theoretical prediction for this profile which is in good agreement with simulation. Finally, we investigate the intrinsic (non-wandering) front width and find results consistent with scaling and field theoretic predictions.